A Handbook of numerical Matrix inversion and Solution of linear equations

A Handbook of Numerical Matrix Inversion and Solution of Linear Equations is intended to be nearly encyclopedic, and was written with the hope that it might provide a single reference source for the “average” scientific pro- grammer with an A. B. and a mathematics major. It attempts to present a straightforward account of a great many numerical methods for the in- version of matrices and solution of systems of linear equations, with emphasis on computer solution. Some of the methods that are not especially useful or practical as digital computer methods are barely touched on, and are included only for completeness, whereas methods that are appropriate for use on digital computers are usually described in greater detail. Few proofs are given, but all should be available in the literature listed in the references. It is assumed that the reader will make extensive use of the glossary, Ap- pendix A, for definitions of unfamiliar or forgotten terminology, and that he will refer to the list of theorems in Appendix B for a summary of basic facts about matrix algebra. Appendix C is intended to provide a variety of test cases as well as methods for generating more. Because the appendices and references are provided as supplementary material, they contain many references, definitions, and theorems not specifically referred to in the text.